Economics 426: Problem Set 8 – Production 经济学生产问题代写 I. Show that if A and B are closed subsets of Rn , then A+B is closed or provide a counter example. (20 pts) II. Show that if A and...View details
ECON5001 Microeconomics Theory
Problem Set 2
微观经济学理论代写 Exercise 1 Draw indifference curves that represent a consumer’s preferences for burgers and coke. Indicate the direction in
Draw indifference curves that represent a consumer’s preferences for burgers and coke. Indicate the direction in which utility is increasing.
1. The consumer has convex preferences and dislikes both burgers and coke.
2. The consumer likes burgers and dislikes coke. If she is served a coke, she will pour it down the drain rather than drink it.
3. The consumer likes burgers and dislikes coke. If she is served a coke, she will drink it to be polite.
4. The consumer likes burgers and coke, but insists on consuming exactly one coke for every two burgers that she eats.
Exercise 2 微观经济学理论代写
Alice’s utility function is U(x; y) = x2y while Steve’s utility function is U(x;y) = x2y + 2x. Do Alice and Steve have the same preference relation?
There are two goods, 1 and 2. You have a total income of I.
(a) Suppose that the government takes away m dollars, regardless of your behavior (This is called a lump-sum tax). Draw the budget line.
(b) Instead, suppose that you could consume good 2 at a price of p2 dollars up to some level x20 and then the government gives you t dollars per unit of consumption of good
2 in excess of x20. Draw the budget line.
(c) Instead, suppose that the government imposes a value tax on each commodity and the tax rate is τ. Draw the budget line. What is the equivalent income loss to the value tax?
(d) Instead, suppose that the government imposes an income tax and the tax rate is τ/(1+ τ). Draw the budget line.
Exercise 4 微观经济学理论代写
For each of the following utility functions, draw indifference curves for different utility levels as indicated. Calculate MRS. Use arrows to show the direction in which utility is increasing.
Suppose Tom can spend his income of $100 among two goods G1 and G2. The unit price of G2 is $1 per unit regardless of how much of G2 he consumes. However, there are quantity discounts available on G1. Whenever she consumes less than 50 units, the price of G1 is $1 per unit. Every additional unit of G1 above 50 is priced at 50 cents. (Assume that G1 and G2 can only be consumed in non-negative quantities). Draw the Budget set.
Exercise 6 微观经济学理论代写
Instead of facing a quantity discount in Exercise (5) suppose instead that higher consumption of G1 is taxed. That is assuming that the price of G1 is always $1. However, every additional unit of consumption of G1 that exceeds 50 units is taxed an additional $1 per unit. Price of G2 remains at $1. Draw the Budget set.
Nicole consumes two goods, X and Y. Her utility function is given by the expression U = 5X2Y. The current market price for X is $20, while the market price for Y is $40. Nicole’s current income is $1200.
a. Write the expression for Nicole’s marginal rate of substitution between the two goods. Interpret its meaning.
b. Write the expression for Nicole’s budget constraint. What is the slope of the budget constraint? Interpret its meaning.
Exercise 8 微观经济学理论代写
Charlie likes both apples and bananas. He consumes nothing else. The consumption bundle where Charlie consumes xA bushels of apples per year and xB bushels of bananas per year is written as ( xA , xB ). Last year, he consumed 20 bushels of apples and 5 bushels of bananas. It happens that the set of consumption bundles ( xA , xB ) such that he is indifferent between ( xA , xB ) and (20,5) is the set of all bundles such that xB = 100/xA .The set of bundles ( xA , xB ) such that he is indifferent between ( xA , xB ) and the bundle (10,15) is the set of bundles such that xB = 150/xA .
(1) Draw the indifference curve passing through the point (20,5). Similarly, draw the indifference curve passing through the point (10,15).
(2) Indicate the set of commodity bundles that he weakly prefers to the bundle (10,15). Similarly, indicate the set of commodity bundles that he weakly prefers to the bundle (20,5).
(3) For each of the following statements about his preference, answer “true” or “false” and explain why.
(4) Is the set of bundles that he weakly prefers to (20,5) a convex set? The set is convex if the consumer weakly prefers averages (or a mix) of the two bundles to either of the original bundles. Explain.
(5) Is the set of bundles that he considers inferior to (20,5) a convex set? Explain.
(6) The marginal rate of substation is the slope of an indifference curve (at a given point). It shows the amount of one good the consumer is willing to give up in order to get a little bit extra of the other good, such that she is indifferent between the old and new bundles. That is, she remains on the same indifference curve. Do the indifference curves you have drawn for him exhibit diminishing marginal rate of substitution? Explain.